gmatt1476 wrote:
King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?
A. 25
B. 30
C. 36
D. 60
E. 150
PS15402.01
No student has a free period.
Thus, all 900 students are taught each period, implying that each period is composed of the same number of 30-student classes.
Every teacher teaches 5 of the 6 periods.
Thus, every teacher teaches exactly 5 classes.
We can PLUG IN THE ANSWERS, which represent the number of teachers.
When the correct answer is plugged in, the total number of students taught each period = 900.
B: 30
Since each of the 30 teachers teaches 5 classes, the total number of classes = 30*5 = 150.
Since these 150 classes are divided equally among 6 periods, the number of classes per period \(= \frac{150}{6} = 25\).
Since each of these 25 classes is composed of 30 students, the total number of students taught each period = 25*30 = 750.
Too small.
D: 60
Doubling the number of teachers from 30 to 60 will double the number of students taught each period from 750 to 1500.
Too big.
Since B yields a result that is TOO SMALL and D a result that is TOO BIG, the correct answer must be BETWEEN B AND D.